Many, maybe even most, of what we are like as human beings derives not from within ourselves but from our relationships—our bonds, our dealings, our links—with others of our kind.

Voyaging canoe seen near Buka Island by French explorers in the last decade of the 18th century. From J.J.H. de Labillardière's atlas published in 1817 and reproduced by courtesy of the Rare Book Room, Library, Field Museum of Natural History, Chicago.

John Terrell

A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space. By Jason Hise at English Wikipedia [Public domain], from Wikimedia CommonsEARLIER I SUGGESTED THAT network relationships have three general characteristics that can be labeled situational, circumstantial, and consequential. I also noted that along with the spatial dimensions of life conventionally called length, width, and depth, we need to add a fourth one called time—thanks to the insights of Albert Einstein and others. We now know that as we make our way from the cradle to grave, we do so not just across something called space. Not just through something called time. Instead, we are traveling within something cryptically labeled by physicists as space-time: the fusion of time with the usual three dimensions into a 4-dimensional space.

I have also proposed, however, that we must add yet another dimension to the menu. Although physicists and others may have their own ways of imagining what this 5th dimension is like, I propose that we should use it to capture the simple truth that a great many things in the universe exist not in some elemental form (such as copper, silver, and gold), but instead as compounds of differing elements linked, tied, or bonded in some way with one another. Classic examples would be sea salt (NaCl), water (H2O), quartz ( SiO2), and ethanol, also known as drinking alcohol (C2H5OH).¹

As physical entities, all of these everyday substances—even water—can be measured in terms of length, width, and depth. We can measure them, too, in terms of time, although often this 4th dimension of reality is ignored on the unspoken assumption that time is unlikely to have a decided effect, say, on a pound of salt, a bottle of spring water, a lump of rose quartz, or a fifth of the finest bourbon (although, come to think of it, time is often said to improve in wonderful ways the taste of both bourbon and a fine wine).

Water molecule. By Benjah-bmm27 [Public domain], from Wikimedia CommonsNow it would be unconventional, even odd, to describe any of these familiar molecular compounds using the language of network analysis. Even so, the character and material existence of each of these substances depends on the particulars of what and how its constituent elements are linked to one another.

Take water, for example, which is the most abundant substance on Earth. Water exists because it is possible for two atoms of hydrogen to be linked to one atom of oxygen by sharing electron pairs. At this basic material level of existence, the preferred way of describing the relationship between hydrogen and oxygen would be to say that water exists when two hydrogen atoms are covalently bonded to one atom of oxygen. Yet why not say instead that water exists as a material substance because two hydrogen atoms are related covalently to one atom of oxygen?

And if we did, what difference would it make?

Problem

Depending in part on how old and fat you are, each of us is somewhere between 50% to 65% water. Perhaps even more surprising, the human brain is around 75% water. Needless to say, facts and figures like these in no way mean that people also are bonded to one another covalently by shared electron pairs.

And yet however golden some of us may seem as personalities when compared with others of our kind, it should be apparent to anyone paying attention to what people are like that each of us is a combination, so to speak, of ingredients. Some of our traits may be more or less unique to each of us alone. Yet many, maybe even most, of what we are like as human beings derives not from within ourselves but from our relationships—our bonds, our dealings, our links—with others of our kind. Humans, too, are composites, blends, mixtures. And more than we might like to accept sometimes, we exist precisely because we are linked socially, emotionally, and materially with others. This is so even when we are still in the womb.

https://www.flickr.com/photos/93413187@N06/8492516706/sizes/l/

However, regardless how true this observation may be, such a statement is just a generalization.

Is there some way to pin down in real terms how much credit (or blame) for what people are like as individuals must be given to their links, bonds, and relationships with others?

Hypothesis

Despite their scientific training and accomplishments, even geneticists, anthropologists, and other scientists today still seem willing to accept the old-fashioned folk belief that people belong to more or less separate and distinct collective “kinds” that can be labeled as “populations.” (These are also sometimes called groups, peoples, tribes, ethnicities, races, and the like.) But does it really make sense to say that human beings naturally come in separate kinds? What is a population? How can we tell whether we are “inside” a population or “outside” it? If they are as real as conventional wisdom assumes, how many of these kinds of things are there “out there” in the real world?

The late anthropologist Fredrik Barth (1969) once famously observed that people can be different from one other in their own ways without having to be cut off and isolated from other people. Contrary to conventional wisdom, in other words, contact and interdependence—i.e., social relationships—do not rule out what generally gets labeled as “human diversity.”

Instead of just accepting Barth’s claim, can we turn this observation into a testable hypothesis about human similarities and differences? Phrased more floridly, is each of us more like a nugget of gold or a drop of water when it comes to what we are like as a human being?

Model-building

Out of all the places on earth where people live, it would not be a flamboyant exaggeration to say the New Guinea region in the southwestern Pacific contains more human diversity than anywhere else on earth. Take language, for example. It is far from easy to count the number of languages extant in this region of the world for two major reasons. First, the island of New Guinea itself (the 2nd largest island in the world) is cut in half by two different nation states. Indonesia rules the western half. The independent nation of Papua New Guinea governs not just its eastern side, but also a great many other smaller islands in the surrounding waters. Papua New Guinea is usually said to have something like 850 or so different languages. The estimated number spoken in the Indonesian provinces on the western side of the island is harder to piece together from available information, but a conservative number would be 250-300 languages. Whatever the actual count, add these various figures together and the amount of linguistic diversity is remarkable.

The second reason is worthy of mention, and that is all I will do here. One of the grand aphorisms in linguistics is this one: “a language is a dialect with an army and a navy.” This saying is often attributed to the Yiddish linguist Max Weinreich, although Weinreich himself never claimed the saying was his. He was evidently just the first person to publish it. In any case, an honest answer to the question “How many languages are spoken on New Guinea?” would have to be the compound question “Who is counting them, how are they being recognized as separate languages, and who cares?”

These are all good questions. Answering them first and foremost calls for having ways to measure relationships in this part of the world not just in terms of length, width, depth, or time, but also in how dependent or independent people happen to be in any given location is this vast and geographically complex part of the world (Figure 1). After all, language is a prime way by which people communicate with one another. (Although I must confess I have always been someone who talks to himself a lot.) It is not unreasonable, therefore, to suspect that focusing on language diversity may give us a good sense of how dependent or independent people in any given place in this region are likely to be.

Figure 1

Based on historical information, it can be said with confidence that people and communities in the southwest Pacific are definitely not isolated from one another despite the scale and geographic ruggedness of these islands. Although I suspect he would choose different words to use today, back in 1983 the human geographer Bryant Allen summarized the state of life in this part of the world succinctly this way (see Figure 2):

Before white contact Papua New Guinea communities were small and very localized. With few exceptions they could provide for themselves all their subsistence requirements from within their own territory. Many men travelled no further than a few kilometers from their birthplaces all their lives. Travel was discouraged by rugged terrain and hostile neighbors. Nevertheless, the country was criss-crossed with well established trade routes along which travelled food, animal products, bird plumes, dogs’ teeth, sea shells, fish, clay pots,
potassium and sodium salt, sago, stone axe blades, obsidian, wicker baskets, wooden dishes, string bags, paints, dyes and coloured earths, as well as art forms, dances, magic, sorcery and new ideas. (Allen 1983: 19)

Figure 2. Some of the major trade route in the Papua New Guinea region (Allen 1983: fig. 6).

Given this historical information, the hypothesis seems worth pursuing that human diversity—including but not limited to language diversity—in this region must somehow be a combination of traits, some local and others more broadly shared. But given the vast scale and geographic diversity of this part of the world, what is it that we should we try to measure first, and how should we try to do so?

Figure 3.

Back in the early 1970s long before today’s personal computers, I wanted to confront this challenge in a way that was feasible given the state of technology then available. Specifically, I wanted to create geospatial maps or models that could be used to estimate what would be the most likely paths or routes for human relocation, interaction, trade, and the like among local communities on the premise that the most probable paths of interisland travel can be estimated given only two measurable variables: distance and land area.

Information can be found elsewhere on how I created what I called back then the “network graph” shown in Figure 3 superimposed over a conventional map of the Solomon Islands (Terrell 1977). The strategy used to create this simplification of the complex spatial geography of the Solomons archipelago was so elementary (Figure 4) that I was honestly worried that my research colleagues wouldn’t take the resulting mapping seriously. Hence I decided on a deliberately pretentious way to label it, one that goes fairly trippingly off the tongue. I dubbed this type of network graph a “proximal-point analysis.”

Figure 4.

I am both delighted and amused to say that not only is this basic network mapping strategy still in use (with or without employing a pencil and a ruler), but it is widely known at least in archaeological circles in Europe as a “ppa analysis” (Amati et al. 2018).

Furthermore, I should note also that a less precise but similar network structure had been independently devised by the biogeographer P. J. M. Greenslade to predict the taxon cycle of faunal migrations through the Solomons archipelago (Greenslade 1968, 1969; Wilson 1961).

What’s next

Human geographers have long been familiar with the effects of distance and population numbers (and thus area) on the probability of human movement, interaction, trade, and the like among people and the places where they live. Back in the 1970s when we were starting to develop network approaches to human diversity, some working then in the Pacific may have thought that what we were doing was simplistic, deterministic, and pointless. It was reported to me by a friend that one well-known archaeologist dismissed what we were trying to do by saying that all an archaeologist really needs is a few good sites to dig. We paid little attention to this sage advice.

Having determined what you want to do, however, can lead to a painful realization. There may be little on hand to do it on. The challenge we faced was frightening and also invigorating. Could we decide not only what we needed to know about, but also where to find it?

John Terrell

UNDER THE BANNER HEADLINE “The Biggest Questions in Science” the well-known writer Madhusree Mukerjee didn’t need to go far out on a limb on 9 May 2018 in Nature or later in Scientific Americanto say something wise although not earth-shattering: “In recent centuries we have learned so much—and such marvelous things—about the worlds around and within us that it may sometimes seem that no nook is left unexplored, no miracles left for us to unravel.” Not so, she ventured. “The truth is, though, that every new discovery leads us to ever deeper questions.”

Following Mukerjee’s lead, the editors at Nature and ScientificAmerican then offered the world, or at any rate the readers of these two publications, a half-dozen lengthy essays by a like number of authors on what they evidently see as the six biggest questions in science today. Why just six? Who knows?

Furthermore, one could challenge the tacit editorial claim that this particular selection of essays is as good as they get. For instance, the opening sentence of the third essay titled “What is consciousness?” reads as follows: “Consciousness is everything you experience.” You don’t have to be a stick-in-the-mud Freudian to suspect this can’t possibly be true. Yet let’s not quibble and get distracted by such a questionable opening thought.

Instead I want to underscore that doing good science first and foremost calls for asking good questions.

Such an observation may come across to you as every bit as obvious as Mukerjee’s pronouncement that every new discovery leads us to ask ever deeper questions. Even so, I hope you will grant me that not all possible questions are equally worthy of careful scientific scrutiny.

For example, I don’t understanding why anyone would take the effort, time, and research funding to do a network analysis to show that being beautiful—whatever one takes beauty to be—can be personally advantageous (O’Connor and Gladstone 2018).

On the other hand, I think it is noteworthy that studying the evolution of life on earth from a relational network perspective can radically change how we envision The Tree of Life (Quammen 2018).

What’s a good question?

As parents often do, my mother had a number of handy sayings she would resort to when I was young and not always the perfect child. One I remember is a keeper: Just because you can doesn’t mean you should. Reading through the abstracts of research papers published in any scientific journal is likely to conjure up this thought more often than not. My own favored way of saying more or less the same thing when it comes to the questions scientists ask is the terse interogative So what?

When it comes to doing network analysis, a more constructive and positive query would be this one: If doing network analysis is the answer, what is the question?

Consider the consequences

As the old saying goes, there is no disputing taste. The big questions in science that rock your boat may not be the questions I’d ask. And vice versa. There is also no gold standard for deciding what makes a question good, bad, or indifferent.

However, it seems reasonable to say that if questions can have answers, then answers may have consequences. Hence one way to judge the quality of a research question is to ask whether those asking it have answers for the So what? question that do more than just hint at what may be the consequences of answering the question they are asking.

After all, asking questions about questions is not only possible, but is at least sometimes wise.

I hesitated long before I put this theory to the test of practice. I knew well that I risked death; for any drug that so potently controlled and shook the very fortress of identity, might by the least scruple of an overdose or at the least inopportunity in the moment of exhibition, utterly blot out that immaterial tabernacle which I looked to it to change. But the temptation of a discovery so singular and profound, at last overcame the suggestions of alarm. I had long since prepared my tincture; I purchased at once, from a firm of wholesale chemists, a large quantity of a particular salt which I knew, from my experiments, to be the last ingredient required; and late one accursed night, I compounded the elements, watched them boil and smoke together in the glass, and when the ebullition had subsided, with a strong glow of courage, drank off the potion.Strange Case of Dr. Jekyll and Mr. Hyde, Robert Louis Stevenson, 1886

What’s the problem?

Another of the essays in Mukerjee’s half-dozen in Nature and Scientific American in 2018 is one titled “How Much Can We Know?” by Marcelo Gleiser. Dr. Gleiser is a professor of philosophy, physics, andastronomy at Dartmouth College. In suitable homage to Heisenberg and his uncertainty principle, he starts off his essay this way:

“What we observe is not nature in itself but nature exposed to our method of questioning,” wrote German physicist Werner Heisenberg, who was the first to fathom the uncertainty inherent in quantum physics. To those who think of science as a direct path to the truth about the world, this quote must be surprising, perhaps even upsetting. Is Heisenberg saying that our scientific theories are contingent on us as observers? If he is, and we take him seriously, does this mean that what we call scientific truth is nothing but a big illusion?

It hardly needs saying he comes around to the less jaundiced view that what we see in the world around us is not nature itself but nature as discerned through data we collect from machines. “In consequence, the scientific worldview depends on the information we can acquire through our instruments.” I suppose if you are an astronomer, this claim rings true, but of course this sentiment is not universally so. I’d even be willing to say such a statement has a pontifical silliness about it.

Nonetheless, who can disagree with his additional claim that science is “our best methodology to build consensus about the workings of nature”? Yet here, too, caution is required. We need to add to this conventional observation the added reflection that it is easy for us humans to fool ourselves into thinking that consensus is the same as truth.

Therefore, to respond to the question raised earlier—If doing network analysis is the answer, what is the question?—I suggest first that even if good research questions in science might be a dime-a-dozen depending, say, on how generous we are in entertaining unconventional ideas, the ecologist Robert MacArthur back in the early 1970s was right: “The only rules of scientific method are honest observations and accurate logic. To be great it must also be guided by a judgment, almost an instinct, for what is worth studying” (MacArthur 1972: 1).

Perhaps your take on MacArthur’s words may be radically different from mine, but for me what he is saying is that having a keen sense of problem paves the way for asking good, maybe even great, research questions about the world and how it works.

What are good plausible answers?

Those who knew him say Robert MacArthur was more than just a fine field ecologist. He was also a pioneer in practicing the art of mathematical modeling in community ecology, island biogeography, and population biology. As he observed with his colleague E. O. Wilson in 1967:

A theory attempts to identify the factors that determine a class of phenomena and to state the permissible relationships among the factors as a set of verifiable propositions. A purpose is to simplify our education by substituting one theory for many facts. A good theory points to possible factors and relationships in the real world that would otherwise remain hidden and thus stimulates new forms of empirical research. Even a first, crude theory can have these virtues. (MacArthur and Wilson 1967: 5)

Modeling reality

If this were a cookbook, the recipe for dynamic network analysis we will be following in the rest of the posts in this series starts as follows:

PROBLEM: begin by stating a well-defined research purpose.

HYPOTHESIS: given what is known or may be plausibly assumed, map out what could be “the permissible relationships among the factors as a set of verifiable propositions.”

With regard to the last item in this opening list, as the late Richard Levins famously wrote a half century ago: “even the most flexible models have artificial assumptions. There is always room for doubt as to whether a result depends on the essentials of a model or on the details of the simplifying assumptions” (1966: 423). And as he went on to say (specifically about biological models, but the lesson still rings true):

Therefore, we attempt to treat the same problem with several alternative models each with different simplifications but with a common biological assumption. Then, if these models, despite their different assumptions, lead to similar results we have what we can call a robust theorem which is relatively free of the details of the model. Hence our truth is the intersection of independent lies.

What’s next

The next post in this series introduces a simple network modeling strategy devised nearly half a century ago that only requires three tools to implement: a pencil, a ruler, and map of whatever part of the world you want to simplify in a way that preserves the essential features of the problem you are trying to grapple with.

References cited

Levins, Richard (1966). The strategy of model building in population biology. American Scientist 54: 421–431.

MacArthur, Robert H. (1972). Geographical Ecology: Patterns in the Distribution of Species. Princeton University Press.

MacArthur, Robert H. and Edward O. Wilson (1967). The Theory of Island Biogeography. Princeton University Press.

O’Connor, Kathleen M. and Eric Gladstone (2018). Beauty and social capital: Being attractive shapes social networks. Social Networks 52: 42–47.

Quammen, David (2018). The Tangled Tree: A Radical New History of Life. Simon & Schuster.

This is Part 9 in a seriesof posts introducing dynamic network analysis.Next up: 10. What?

John Terrell

WHAT CAN NETWORK ANALYSIS ACCOMPLISH beyond data mining, mapping, and fancy (or plain) visualization? Not an easy question to answer. The published literature on networks is enormous. I am going to focus now, therefore, only on social network analysis with the understanding that later I will have things to say, as well, about other applications.

If all you have is a hammer

Consider the popular expression often attributed (wrongly, it seems) to Mark Twain: “if all you have is a hammer, everything looks like a nail.” Having recently surveyed the last ten years of research papers published in the journal Social Networks, I think it is possible to say a few things in general about the state of this research pursuit. While there are numerous exceptions, of course, many doing social network analysis seem so committed to the established structuralist view of networks that this saying might just as well be rephrased as “if all you have is a network, everything looks like a structure.” Since what I mean by saying this is probably far from clear, here’s the issue I have with this narrowly focused sociological take on network analysis.

There are only so many ways a given number of things (call them N) can be connected together, mathematically speaking. For example, the maximum number of simple ties among N=10 things is N(N-1)/2, i.e., 45. Therefore, even if we must know for some excellent reason how N=10 things are linked (that is, “structured”) in ways equal to or less than this maximum number of ties, surely this cannot be all we need to know to understand why these ten things are structurally connected with one another in one way or another.

Yet what I have taken away from reviewing the past ten years of research papers in Social Networks is that the focus of much of the work being reported is often more about methodology—the “hammer,” so to speak—than about what to build with it worth the investment of time, money, and effort.

A limited tool kit

Here’s another way of saying what I just said. While going through articles in this journal I was repeatedly surprised that network analysis seems to be used only rarely to model and test explanatory research hypotheses. Instead, even when real-world data are included as part of the exercise, what is often invoked are a small number of social network’s own proprietary analytical concepts labeled as “parameters” and “social processes” used in ways which are not only descriptive but often also seemingly explanatory (e.g., Fitzhugh and Butts 2018). Typical examples are these: centrality, density, transitivity, clustering, reachability, and so forth (Hanneman and Riddle 2005). I won’t try to explain here what these are, but include links that describe them in some detail.

I find it is hard to know what to make of these so-called parameters and processes. For instance, here is what one well-known online handbook tells us about the sociological concept of power: “All sociologists would agree that power is a fundamental property of social structures. There is much less agreement about what power is, and how we can describe and analyze its causes and consequences.” Following this candid but confusing observation, we are then told:

Network thinking has contributed a number of important insights about social power. Perhaps most importantly, the network approach emphasizes that power is inherently relational. An individual does not have power in the abstract, they have power because they can dominate others—ego’s power is alter’s dependence.

What I want to underscore about this assertion is that apparently such an observation is not being offered to us as a research hypothesis suitable for testing against data. Instead, we are evidently being asked to accept this portrayal of power, whatever you take it to be, as a statement of truth.

Why do network analysis?

The passages quoted above come from a standard and extremely helpful introduction to social network methods by Robert Hanneman and Mark Riddle published back in 2005. This guide for the perplexed is still freely available on the Internet today. These authors are careful to tell us what they see as the three main reasons for using the methods they describe. Here they are, rewritten to abbreviate them:

The matrices and graphs at the heart of network analysis are compact and systematic ways to manage information and manipulate data efficiently so we can detect structural patterns that otherwise can be tedious to document and hard to see;

since these methods are quantitative and mathematical, we are able to use computers to analyze networks data, even massive amounts of it; and

these rules and methodological conventions can help us do more than communicate effectively; they can also help us discover things in our data we might not even think to look for using only words to describe and summarize the relationships reflected in the information we have.

You may disagree, but I think these three strengths are basically those I have previously labeled as mining, mapping, and visualization, although I haven’t yet mentioned using computers.

In any case, I am certainly not alone in thinking there is more to social network analysis than just these three strengths. As these authors themselves say in the afterword that concludes their handbook:

The basic methods of studying patterns of social relations that have been developed in the field of social network analysis provide ways of rigorously approaching many classic problems in the social sciences. The application of existing methods to a wider range of social science problems, and the development of new methods to address additional issues in the social sciences are “cutting edge” in most social science disciplines.

Unfortunately, they say nothing at all about what these problems and additional issues may be. Their closing words are simply these:

we have not touched on very much of the substance of the field of social networks—only the methodologies. Methods are only tools. The goal here is using the tools as ways of developing understanding of structures of social relations. The most obvious next step is to read further on how network analysis has informed the research in your specific field. And, now that you are more familiar with the methods, you may see the problems and possibilities of your substantive field in new ways.

Integrative networks

Despite these inconclusive words at the end of this influential handbook, social network analysis has never been solely about mathematical methods and formal procedures. In 2012, for example, an issue of Social Networks was entirely devoted to exploring the common ground between social network research and geographic spatial analysis even though it was acknowledged that “the formal integration of social network and spatial analytic strategies remains relatively underdeveloped in the literature” (Adams et al. 2012: 1).

Although there have been advances since then such as the use of adaptive network modeling in restoration ecology (Raimundo et al. 2018) and in understanding how violent crime effects inter-neighborhood community patterns in Chicago (Graif et al. 2017), this goal still seems a long way off.

Does this matter? Perhaps not if all that you want to do is map and visualize the relationships among N things, people, or places to offer plausible interpretations of the observed structural arrangements, but is this the most that network analysis can hope to achieve (Doreian and Conti 2012)?

Over forty years ago (Terrell 1977), I suggested that similarities and differences among local human populations reflect the workings of an integrated complex of variables and relationships that can be idealized as a geographic system (Figure 1).

Figure 1. “The concept of geographic systems can be described using an elementary model to depict how local populations and the habitats they occupy may all be seen as interrelated within a comprehensive network of interactions. The concept itself may be defined as follows: a geographic system is the interactive configuration among the size, distribution and interaction structure of a set of local populations and the elements and interaction structure of the area of their occurrence, analysed as a complex of intercommunicating variables within which a change in any one variable or relationship is likely to effect changes, of a greater or lesser degree, in all the others. It probably is not necessary to add that such a complex of variables and relationships is unlikely to respond only to single causes, although changes in some dimensions may be more influential on the system as a whole than changes in others” (Terrell 1977: 65).

Back then I knew that from this integrative perspective it wouldn’t do to reply on categorical units labeled for convenience as “populations,” “habitats,” “geographic regions,” and the like. At this same time, therefore, I began to explore using network approaches inspired by work in locational geography (Terrell 1976). As shocking as it may seem to network sociologists, I knew absolutely nothing at that time about the work of Harrison White, one of the founders of the modern sociological networks tradition, even though I had been an undergraduate and later a graduate student at Harvard. The distance between Anthropology and Sociology there in Cambridge, Massachusetts, back then was not geographic but social and cultural.

I was also inspired by ecology and biogeography as practiced then. But here, too, I saw one had to be careful not to borrow from other disciplines without being watchful. As I wrote in 1977:

the geographic system concept resembles that of an ecosystem and encompasses the trophic or food relations between man and his environment which are specifically explored by human ecologists. The concept, nevertheless, is intended to be more inclusive than that of an ecosystem, in order to avoid the a priori assumption that an analysis of the interactions within and among human populations can be reduced to a study of the trophic, biochemical and species structures of their environment and the functioning of those structures. (Terrell 1977: 65).

While I won’t try to detail the reasons, I was also dissatisfied with the idea that the Earth can be subdivided into geographic regions, and with the convention back then that networks are systems (nowadays I would be more vocal about saying that systems are networks, but not all networks are systems).

A geographic system . . . is a set of biological and ecological elements, their structural relationships, and their functional operation. . . . [W]hile geographic regions have spatial boundaries by definition, geographic systems do not. All the communities living within a region may be usefully called a regional population, yet it is conceivable and even likely that a given region, defined spatially, may house two or more fairly distinct “system populations” which interact little if at all among each other.

Even thus qualified, I felt more needed to be said, and followed these observations with words of caution. “The world in all its complexity is not, after all, a mosaic of discrete parts or ‘regions'” (Terrell 1977: 66).

Dynamic networks

Given the hindsight of 40+ years, I would now visualize what I was trying to say differently (Figure 2). Had it also been a low-cost publishing option back then, I undoubtedly would have opted to use color, not that doing so makes much difference except possibly in the visual appeal of the model:

Figure 2

What either version of this conceptual model hopefully conveys is that while one could be committed professionally to researching just a single relational dimension in this complex of relationships—as it seems most doing social network analysis today prefer to do—if you want to learn not just how social relations are structured but also why, then it would be naive to assume what you are observing can be explained solely by social properties and processes.

I have argued previously that something can be called a “relationship” if what you have in mind is repetitive, situational, contingent, and consequential. Additionally, I have also noted that two other dimensions need to be added when the relationships are social: intentional and purposeful.

But this is not all. Without any explanation I added earlier that another dimension needs to be included: adaptation (Figure 3).

Figure 3

I will have much to say about adaptive networks in future posts in this series. At this point, since this one is longer than I like already, let me just give you a simple example of what I have in mind.

From a sociological perspective, what happens in a hospital operating room is unquestionably an example of a small functioning social network. Ignoring the role of the patient on the table for a moment, everyone in the room has a role to play and is related to everyone else in clearly defined ways (much more clearly defined, by the way, than would be normal outside the medical and legal environment of the operating theater).

It seems reasonable that if one wanted to, many of the standard parameters and social processes favored in sociological network analysis can be employed to mine, map, and visualize what is going on over the supine (or prone) figure lying on the operating table. But if one then stopped paying attention to the work being done, what would be the point of even just being there to witness the operation?

What would soon become painfully apparent if you stayed around longer is that as the surgical team proceeds with the operation at hand not merely because they want to (what they are doing, in other words, is obviously intentional), but also because they hope to achieve a particular outcome (the operation is, after all, purposeful), who does what, why, when, how, and even whether evolves dynamically to meet the changing contingencies of what they come across once the patient is anesthetized, opened up, and the work begins in earnest.

What’s next

What is happening in this hypothetical operating theater is a simple example of what I want to talk about in future posts in this series when I am exploring with you not just how but also why it is good to study networks of human engagement between things, places, and people as dynamic, adaptive, evolving strategies—not just structures—for survival.

When you are asking good questions and trying to use network analysis to answer them, the focus should not only be on nodes and linkages, but also on exploring the consequences of the relationships being examined.

https://pxhere.com/en/photo/1084246

John Terrell

IT SEEMS LIKELY MANY TODAY on hearing the word “network” may assume you must be talking about an Internet outage or service delay. It seems less likely they will think you are referring to something as rarefied as network analysis.

However, people devoted to using social media in creative ways, and those paying attention to the news each day, may have at least a beginner’s understanding of the currently popular uses of this technical approach to the mysteries of the universe. Even they, however, may be minimally aware of the weaknesses, the limitations, of such research.

Furthermore, should some inquisitive souls venture as far as reading a textbook on this topic, they may decide that such books, undoubtedly impressive for their mathematics and node-link diagrams, are more about “how to” than about “why?” or “so what?”

Therefore, what are some of the demonstrated strengths of network research? What currently are some of the known weaknesses? Is there anything that can be done to overcome the latter?

Said more simply, why do network analysis?

Data mapping and visualization

Graph representing the metadata of thousands of archive documents, documenting the social network of hundreds of League of Nations personnel. (By Martin Grandjean [CC BY-SA 3.0 , via Wikimedia Commons.)Network diagrams can be visually striking, even intimidating. Come across one or two of these visualizations in a research article, and even if you don’t know all that much about the science involved, it’s hard not to be impressed.

While granting, therefore, that network diagrams can be both pretty and impressive, evidently little is yet known about how successfully people are able to interpret such visualizations. Nor it it clear whether or when network visualizations actually improve human understanding and problem-solving. There is, however, some evidence suggesting that both data tables and network visualization are more effective ways of communicating information and scientific findings than conventional text descriptions (Welles and Xu 2018).

“The change of community structure after applying the schneider’s method [23] on the dolphin network. Fig. 1(a) presents the community structure of the dolphin network with N = 62 dolphins and M = 159 co-appearance of them. The network can be divided into 5 communities, which are marked as different colors. Fig. 1(b) presents the onion-like structure of the improved network. The community structure of the network is greatly changed. Fig. 1(c) shows the clear community structure of Fig. 1(B), i.e. the improved network. The first two figures are drawn by the Gephi automatically, while the vertices in the last figure are separated by the colors manually. The social network of 62 bottlenose dolphins was observed by Lusseau [30]. The dolphins lived in Doubtful Sound, New Zealand. Lusseau collected the data of dolphins according to his field studies of dolphins for two years. The ties between dolphin pairs are established by the observation of the statistically significant frequent association.”(Yang et al. 2015)

Data mining

Anyone shopping nowadays online at companies like Amazon have firsthand experience with the ability these firms now have using relational algorithms to track you, your tastes, where you have been on the Internet, and your prior purchases. What am I referring to? The enterprising phrase “customers who bought this also bought” that is now standard & usual at commercial websites.

Mining what is popularly called “big data” culled off the Internet in this fashion to find correlations and patterns of association is proof enough that relational thinking can have highly profitable payoffs—even when the final product is not an attractive network visualization but instead an enticing and strongly personalized buying recommendation.

If relational data mining like this sounds more than a just little creepy to you, fair enough. The self-serving, some would say malicious, misuse of personal information mined from 87 million Facebook accounts by a company called Cambridge Analytica during the 2016 presidential election in the United States should be more than enough to convince even the most hardened skeptics that data mining using network algorithms can be more than a trivial pursuit.

“Social media analytics is the process of gathering data from stakeholder conversations on digital media and processing into structured insights leading to more information-driven business decisions and increased customer centrality for brands and businesses” (http://www.wikiwand.com/en/Social_media_analytics).

Correlation or cause?

While some purists debate whether statistically speaking “an association” is or isn’t the same thing as “a correlation,” one of the fundamental clichés of statistics is the quip that “a correlation [or association] is not a cause.” The logic behind this observation is straightforward. Saying something (call it A) is correlated with something else (B) just means: if A, then also B with some likelihood or degree of probability. For example: if you like A enough to buy it, then you may also want to purchase B, which the analysis of large amounts of buying data has revealed is something often also bought with it.

Correlations are rarely absolute or perfect. Even when Amazon or some other company lets you know other people who bought this also bought that, buying the latter may be something you’d never ever dream of doing. But given how often Amazon knows for sure that other people have also bought B, it is not unreasonable to think you might be willing to do so, too.

Note, however, that nowhere in the logic of “if A, then B” is it stated why the two are likely to be purchased together. Obviously if Amazon also knew what causesthe pairing of A and B,” the odds of getting someone to buy both might be greatly improved.

In any case, the lesson for us remains unchanged. Just because A and B are correlated doesn’t mean we know why or how they are. Nor do we even know when they are likely to be.

Yes, often comparison of A and B can suggest possible reasons. Both may be similar in character or for a similar purpose. For example, A is a window air conditioner, and B is a steel support bracket for this type of air conditioner. Or A is a book about sexual behavior, and B is something risqué from Victoria’s Secret. Yet while similarity may often be a useful clue, similarity and cause are not one and the same thing.

Constraints and opportunities

Although perhaps not always obvious, a correlation is a kind of pattern. Hence data mining, mapping, and visualization are ways of finding and illustrating not just dyadic correlations between A and B, but also more complex forms of relational patterning within samples of information about this, that, or something else (commonly referred to as data sets). On the face of it, therefore, if it is true that a correlation is not a cause, then so too, it should be true that a pattern is not a cause.

Or maybe complex patterns can be, at least sometimes? It is conventional to say that the goal of networks research is to learn how the patterning of ties within social networks—in the jargon commonly used, the structure of such networks—shapes human behavior (Scott 2000: 19).

Given the familiar old saying “it’s not what you know, it’s who you know,” this possibility may hardly seem worth mentioning. Doesn’t everybody know that the patterning of their relationships with others can often make or break the best-laid schemes o’ mice an’ men? Or as Stephen Borgatti and his colleagues recently expressed what would appear to be this sentiment in a less poetic way:

a generic hypothesis of network theory is that an actor’s position in a network determines in part the constraints and opportunities that he or she will encounter, and therefore identifying that position is important for predicting actor outcomes such as performance, behavior or beliefs. (Borgatti et al. 2013: 1)

If we grant at least for now that the patterning of social ties within a social network can “in part” (as these authors say) determine constraints and opportunities, then doesn’t this mean that network structure can be causal, at least some of the time? If so, then is proving this exception to the general rule that a correlation (or pattern) is not a cause more than adequate justification for pursuing networks research? Or is this justification for this kind of research making too much out of too little?

You guessed it. The question I just asked was a leading question. Surely there must be more to be gained by doing network analysis than just proving over and over again that one’s success depends on who you know, not what you know. Or maybe not?

Limiting assumptions

For me, one of the surprising limitations of many published applications of social network analysis is the evident focus not on what, when, and why the individuals or groups being studied do what they do in their actual relationships with one another, but instead on what Stanley Wasserman and Katherine Faust (1994: 8) have described as “the characteristics of the network as a whole.” Or as they have also phrased this notion: “To a large extent, the power of network analysis lies in the ability to model the relationships among systems of actors” (1994: 19).

Their commitment to such a research agenda is shared by many others doing social network analysis (Knox et al. 2006). In practice, such an agenda leads one to define the “unit of analysis” not simply as people and their relationships with one another, but instead as that vague collective something popularly called the “group”—which Wasserman and Faust are willing to define for us as “the collection of all actors on which ties are to be measured” (1994: 19).

Such a definition of what social network analysis focuses on might be more understandable if they just came out and told us that the word “group” simply means what statisticians label as a “sample.” But evidently this is not what Wasserman and Faust (and others doing network analysis) have in mind. When they write about “systems of actors,” what they want us to take these words to mean is something far more categorical:

A system consists of ties among members of some (more or less bounded) group. The notion of the group has been given a wide range of definitions by social scientists. For our purposes, a group is the collection of all actors on which ties are to be measured. One must be able to argue on theoretical, empirical, or conceptual criteria that the actors in the group belong together in a more or less bounded set. Indeed, once one decides to gather data on a group, a more concrete meaning of the term is necessary. (Wasserman and Faust 1994: 19)

These authors do go on to tell us that dealing with such groups presents social scientists with “some of the more problematic issues in network analysis, including the specification of network boundaries, sampling, and the definition of group” (1994: 19–20). But here’s the big question. If you want to do network analysis, is it necessary to focus on groups? Why can’t the focus be on nodes and linkages? And on causes and consequences more telling, more interesting, and perhaps more mysterious than just what can be made of who we know?

What’s next?

I am hoping you agree with me that I haven’t as yet put our collective finger on why doing network analysis is a good thing to do. I will offer you in the next post in this series the basics of what I see as a better reason. Before going on to do so, however, I want to plant two thoughts in your mind.

First, it’s a big mistake to believe that network analysis has to be about studying something called “the whole network.” Given even the most basic math (N=2n), it is obvious that as the number of nodes increases, the complexity of “the whole” can grow so swiftly that practically speaking, the best any one can do is study samples, not groups or wholes however defined.

Second, if you are really interested in asking good questions and trying to use network analysis to help you try to answer them, then not only should the focus be on nodes and linkages “down on the ground,” so to speak. But also on exploring the consequences of the relationships, human or otherwise, under observation.

In particular, as I will discuss in the next post, we need to add to our classification of networks another column and label it “adaptive.”

John Terrell

AS AN ANTHROPOLOGIST WHO FOR DECADES has been studying how we humans deal with one another and the world around us, I find it fascinating that experts writing about networks and network analysis evidently have difficulty using what I like to call relational thinking.

Here again are the definitions of the two modes of thought I offered in an earlier post in this series:

Categorical thinking assumes things exist apart from one another, and may then become connected with one another. Relational thinking assumes instead things exist because they are connected.

As evidence of the continuing appeal of categorical thinking even in networks science, here is an answer to the question “What is a social network?” given by David Knoke and Song Yang, two of the leading writers on social network analysis. “A social network is a structure composed of a set of actors, some of whose members are connected by a set of one or more relations” (Knoke and Yang 2008: 8).

Here is another definition, this time by John Scott, also a leading writer in this field, similarly implying that social networks are a particular class of things within the general category called structures. “Social network analysis emerged as a set of methods for the analysis of social structures, methods that specifically allow an investigation of the relational aspects of these structures” (Scott 2000: 38).

https://pixabay.com

In both of these definitions (there are others I could give you), the authors are evidently assuming that there is (1) a class of things called social structures* within which (2) people relate to one another in distinct ways making it possible to (3) isolate what they are doing and then label them as “actors” operating within a particular kind or type (i.e., category) of structure.

From the relational perspective I am writing about in this series, however, these supposed structures only exist when—or perhaps I should say through—the relational acts or events that the identified actors are participating in.

It would be more than simply metaphorical, therefore, to say that networks may have more in common with thunderstorms than with the sorts of things one usually thinks of when somebody uses the word “structure.”

Houses, hotels, banks, and boardwalks are all clearly structures. Why use this word also to talk about social networks?

A little history

Scott has reviewed in some detail the history behind why experts in social network analysis see networks as structures of a certain sort. Put briefly, contemporary network analysis is rooted in the 20th century development of mathematical graph theory and structuralist approaches to social organization in sociology and social anthropology. As Scott has concluded: “It is undoubtedly the case that social network analysis embodies a particular theoretical orientation towards the structure of the social world and that it is, therefore, linked with structural theories of action” (Scott 2000: 37).

“Johnson’s algorithm is a way to find the shortest paths between all pairs of vertices in a sparse, edge-weighted, directed graph. It allows some of the edge weights to be negative numbers, but no negative-weight cycles may exist. It works by using the Bellman–Ford algorithm to compute a transformation of the input graph that removes all negative weights, allowing Dijkstra’s algorithm to be used on the transformed graph. It is named after Donald B. Johnson, who first published the technique in 1977.” By David Eppstein [Public domain], from Wikimedia Commons (https://en.wikipedia.org/wiki/Johnson%27s_algorithm).He is not alone, however, in saying also that “social network analysis is an orientation towards the social world that inheres in a particular set of methods. It is not a specific body of formal or substantive social theory” (page 37).

Perhaps you are like me, and you react to this disclaimer as an example of intellectual artful dodging. Can “methods” really exist apart from ideas and assumptions—also known as “theory”—about the world around us?

Methods and theory

Not everyone writing about network analysis would agree that there is a divide between methods and theory. Stephen Borgatti, Martin Everett, and Jeffrey Johnson, major voices in this academic arena, have taken specific aim at such a claim: “some social scientists, unfamiliar with formal theorizing, have misconceived of the field as a methodology.” They acknowledge that network analysis has cultivated a distinctive mathematical methodology, but we shouldn’t let ourselves be fooled by the formality of these methods: “the theoretical concepts that are so emblematic of the field, such as centrality and structural equivalence, are just that: theoretical concepts that are part of a distinctive approach to explaining the social world” (Borgatti et al. 2013: 10).

In the next post in this series, I will begin exploring the ways in which network analysis can help us both ask and then try to answer well-formulated research questions in the social and historical sciences.

Right now, however, I only want to say that both of the examples these three co-authors offer us in this quotation—centrality and structural equivalence—strike me as far from compelling evidence that there is more to network analysis than just the analytical methods used.

However, there is an obvious question still needing an answer.

What is a network?

Just as the proof of the pudding is in the eating, so too, a definition of what something is supposed to mean is only as good as it proves useful. In a real sense, therefore, this entire series on dynamic network analysis could be seen as an extended dining experience (yes, admittedly a rather unconventional analogy). Even so, we need at least a working definition of what is a network, and I suggest this one might do at least at the start:

A network is an interrelated series of events having consequences affecting the likely repetition of those interactions.

At this stage in this series, I only want to point out a few of the implications of such a definition.

First, just as it takes two to tango, so too, it takes at least two people, things, or places to form a network, i.e., ≥N=2. As discussed previously, the events constituting a dyadic network relationship must be repetitive and not randomly so. Furthermore, what happens as part of such a relationship is dependent at least to a degree on the conditions under which the events occur. Differing situational conditions may give rise to differing interactions. Moreover, when interactions happen may be contingent on what has occurred since the last event in the relationship that has possibly changed the situation and the particulars of the interaction.

Second, while mathematicians may have fun solving abstract mathematical problems using graph theory, it is probably fair to say that many, maybe most, people doing network analysis are not doing so for abstract reasons. I am not alone in thinking that what makes network analysis worth doing is minimally the prospect that such analyses can help us pin down in real-world situations the consequences, positive or negative, of networked interactions.

Figure 1

A basic classification of networks

Therefore, as suggested in Figure 1, it can be argued that networks generally all have the three dimensions I have been labeling as situational, circumstantial, and consequential.

However, when it comes to social network analysis, we need to add the dimension of intentionality, a dimension only briefly mentioned in an earlier posting in this series. Furthermore, the intentionality of social interactions (events) between two or more individuals (network analysts seem to favor calling them agents or actors) is not limited solely to our own species. Ask any dog, cat, or wolf of your acquaintance should you have doubts that this is so.

This having been said, it is also important to recognize a distinction that can be usefully drawn between relationships that are intentional—people and other clever animals can cooperate, for instance, to get things done—and networks that are, in addition, purposeful: they are designed as networks of interactions to get things done even when the intentions of the individuals involved in such networks vary.

Perhaps one of the most exotic examples of such a purposeful network would be the ancient trade routes of the Silk Road connecting East with West. Or its modern and sinister namesake, the black market for illicit drugs hidden on the Internet. Another shameful example would be the water supply system of the city of Flint, Michigan.

What’s next?

As I will be exploring in later posts, many analysts are chiefly interested in studying networks that have been specifically designed by those involved to accomplish such larger objectives. As the next step in this series, however, I want to ask what studying networks is good for.

* “From the view of social network analysis, the social environment can be expressed as patterns or regularities in relationships among interacting units. We will refer to the presence of regular patterns in relationship as structure” (Wasserman and Faust 1994: 3).

Instead of seeing networks as systems or structures, it is useful as well as more truthful to describe dynamic network analysis as the study of relational events in time and space of differing character and probability.

John Terrell

DEFINITIONS OF WHAT IS A NETWORK differ in their wording and focus, but a common theme is that different types of relationships give rise to different types of networks.

So if we measure friendship ties, we have a friendship network, and if we also measure kinship ties among the same people, we have both a friendship network and a kinship network . In the analysis we may choose to combine the networks in various ways, but in reality we have two networks. (Borgatti et al. 2013: 3)

In response to such a statement, all I can say is “Oh, really?” The assumptions embedded in these seemingly straightforward words are fairly typical of how network analysis is commonly defined by experts as a way to study the world and our place in it. They are all questionable.

An example of a social network diagram. By Wykis [Public domain], from Wikimedia CommonsWhat, for example, is “friendship” (Terrell 2014)? Is it even possible to have a single and consistent right answer to such a question so that every friendship included in a network of friendships is predicated on the same or at least comparable human feelings, commitments, and acts? Additionally, as social anthropologists know well after many decades of study and debate, don’t even try to see “kinship” as a universally consistent type of human social engagement.

What is a relationship?

Let’s reflect a moment on what I just wrote. Except as an academic exercise, does anyone honestly believe the nuanced relationships that humans have with one another can be usefully seen as a layering of separate networks? So much so, that all of the networks included in any given social network analysis are somehow layered together in a fashion that might be described as some sort of “social sandwich”—to offer an admittedly peculiar simile?

You can probably tell without my having to say so that I want to offer you another way to think about networks and doing network analysis.

Networks are a way of thinking about social systems that focus our attention on the relationships among the entities that make up the system, which we call actors and nodes (Borgatti et al. 2013: 1)

Instead of seeing networks the way most analysts do as systems (Kolaczyk 2009: 2) or structures (Scott 2000: 4), I will show you how it is useful as well as more truthful to describe dynamic network analysis (DYNA) as the study of relational events in time and space of differing character and probability. Importantly, whether the events being analyzed are predictable enough to characterize their co-occurrence as a “system” or “structure” is a matter to be investigated as part of any dynamic network analysis, not something to be assumed at the beginning of study.

Before exploring all this with you, however, I first need to tell you what I mean by the word relationship.

Begin at the beginning

Let’s take things one step at a time. Let’s begin by revisiting what Carlo Rovelli has told us about electrons that got him into trouble with Lisa Randall:

Electrons don’t always exist. They exist when they interact. They materialize in a place when they collide with something else. The “quantum leaps” from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another.

Lightning fill in the blank

I don’t think it would be stretching the point too far to say lightning can be said to exist or not exist in a similar way. As helpfully described by the National Severe Storms Laboratory:

Lightning is a giant spark of electricity in the atmosphere between clouds, the air, or the ground. In the early stages of development, air acts as an insulator between the positive and negative charges in the cloud and between the cloud and the ground. When the opposite charges build up enough, this insulating capacity of the air breaks down and there is a rapid discharge of electricity that we know as lightning. The flash of lightning temporarily equalizes the charged regions in the atmosphere until the opposite charges build up again.

To the human observer, the potential for a bolt of lightning to occur is only something suspected, something lurking in the background, so to speak, before the actual discharge. But the discharge finally neutralizing the imbalance in positive and negative charges that has been developing on the sly doesn’t take place until the relationship between the positive and negative sides of the imbalance finally materializes with what can often be a spectacular display of nature’s given ways.

The famous opening words of a novel by Edward Bulwer-Lytton published in 1830 that are now notorious as an example of purple prose (i.e., overly melodramatic writing). https://www.smith.edu/libraries/libs/rarebook/exhibitions/dickens/16-paul-clifford.htm

Yet the potential for such a dramatic and utterly natural demonstration of light, sound, and at times destructive effect had been there long before this event takes place.

This simple fact raises a basic question. If lightning is the consequence of a growing imbalance between positive and negative electrical charges, say, on “a dark and stormy night,” then what makes this kind of dyadic relationship in nature different from the sorts of relationships that can develop between friends, colleagues, and loved-ones? And what does all this have to do with network analysis?

Repeat after me

https://www.flickr.com/photos/bwtownsend/4887134484

Despite the old saying, it is a well-known fact that lightning can strike the same place more than once. As one storm enthusiast on the Internet has commented, given enough time, this outcome is actually inevitable. He adds, however—and more to the point I want to make in case you are wondering why on earth I am still talking about lightning—the electrical activity in the storm that produced it may generate another strike as soon as as the imbalance has again grown strong enough. Once this happens, a previously hit location again becomes fair game as a recipient of the next discharge. If this weren’t so, there would be no practical need for installing lightning rods on tall buildings and such like.

Being fair game in a relationship is hardly grounds for claiming as well that the cloud in question has formed some kind of a relationship with the location previously hit. Nor is there any sure way to predict whether the same cloud will strike the same place. Maybe another cloud that same day or sometime in the near or distant future may also strike the same place. But there is no guarantee when, and there will be absolutely no connection—no relationship—between the first responsible storm and the later culprit cloud involved.

So here then is one critical difference between the kind of patterned and (seemingly) repetitive type of dyadic event in nature called a lightning strike and the kind of patterned dyadic relationship that occurs in networks of many types, human and otherwise: a network relationship however materialized is not just dyadic but also repetitive.

Relational data . . . are the contacts, ties and connections, the group attachments and meetings, which relate one agent to another and so cannot be reduced to the properties of the individual agents themselves. Relations are not the properties of agents, but of systems of agents; these relations connect pairs of agents into larger relational systems. (Scott 2000: 3)

What else is involved?

What else does it take to turn a repetitive dyadic relationship between two things, people, or places into a broader network relationship? The easy answer would that there is a lot that can come into play. However, there are at least three critical elements in addition to the requirement that the relationship needs to be repetitive and more than just randomly so. What are they? I like to label them as situational (or circumstantial), contingent, and consequential. Let’s consider each in turn starting with the first.

Situational—It is conventionally said in text books about network analysis that there are two basic kinds of data about this world of ours, attribute data and relational data. The former is said to be information about the properties, qualities, or characteristics of the two entities ( for example, the individuals or groups involved) in the dyadic relationship being analyzed—classically, the sorts of information that can be quantified, classified, and analyzed using the many statistical tests of significance that have long been available and are nowadays fairly easy to run on most computers.

https://www.gutenberg.org/files/11027/11027-h/images/011.jpg

Relational data, on the other hand, is information about the linkages, contacts, and connections (called “edges” or “ties” in network analysis) among the entities (called “nodes” or “vertices”) being studied. All well and good, but as we will be discussing in this blog series, when the entities in particular are individuals and groups of people, for instance, the characteristics of interest in any given study often vary depending on the particulars of the situation—the context—they are dealing with. The relationship between Rapunzel and the prince who courted her in the famous fairy tale, for instance, is situationally quite different from what most lovers must deal with to be with one another.

Contingent—Similarly, when and perhaps even whether a relationship is maintained over the course of time may often be contingent, or dependent, on the situation at any given moment on either, or both, sides of the relationship. For instance, whether you flee from what has been your home and seek refuge elsewhere when faced with an environmental disaster or political turmoil may be contingent on whether you have reason to believe there is someone who will be there at the end of your journey who will take you in and help you survive.

A Yemenite family walking through the desert to a reception camp near Aden, 1 November 1949. [Public domain], via Wikimedia Commons] Part of the Jewish exodus from Arab and Muslim countries. “Between June 1949 and September 1950, the overwhelming majority of Yemen’s Jewish population was transported to Israel in Operation Magic Carpet. After several waves of persecution throughout Yemen, most Yemenite Jews now live in Israel, while small communities are found in the United States and elsewhere. Only a handful remain in Yemen.” https://en.wikipedia.org/wiki/Yemenite_Jews

Consequential—Thirdly, relationships may be as seemingly trivial as saying good morning to your neighbor when you go outside to pick up your morning newspaper, but network analysis is a way of pinning down and understanding how relationships can have consequences of real significance, even in instances such as remembering to say hello to a neighbor that most times may seem inconsequential, but not always. It not only takes a community to raise a child, but being on good terms with your neighbors can be highly consequential, for example, when you need to raise a new barn, say, to replace one that burned to the ground after it was struck by lightning.

What about intentional relationships?

Alice in Wonderland by George Dunlop Leslie (1835-1921). Public domain, via Wikimedia Commons

When it comes to the analysis of human relationships, there is no doubt whatsoever that more needs to be considered than just the four relational dimensions noted so far: repetitive, situational, contingent, and consequential.

The relationship between a parent and child, for instance, not only exhibits all four of these characteristics, but is also a motivated or intentional relationship, for better or for worse. Moreover, we humans are not the only creatures on Earth capable of forming and maintaining intentional relationships, as anyone who has ever worked with dogs knows well.

Clearly, therefore, there is more to be said about what is a relationship. However, it is now time to begin asking a similarly basic question. What is a network of relationships?

This is the topic of my next blog in this continuing series on dynamic network analysis.

The Wilderness Hunter: An account of the big game of the United States and its chase with horse, hound and rifle, by Theodore Roosevelt (1903). By Internet Archive Book Images (No restrictions), via Wikimedia Commons

John Terrell

AFTER YOU HAVE SENT to them a carefully collected sample of your spit or a used buccal swab along with your PayPal information, commercial DNA testing companies are likely to send back to you what they have found therein reported as your very own personal “ethnicity estimates“—usually expressed as percentages of this-and-that such as 43% West European, 18% Scandinavian, 6% Irish/Scottish/Welsh, 3% Finnish/ Russian, etc. all adding up to 100%.

If you go online to find out what on earth these percentages are telling you (for example, here) you are likely to get a great deal of misinformation.

Stay tuned to SCIENCE DIALOGUES for a penetrating critique of these pesky little percentages and the less than wonderful racial assumptions lurking within them.

John Terrell

CATEGORICAL THINKING, which I wrote about in the first two posts in this series, may at times be too pat for our own good, but this pragmatic (although potentially knee-jerk) way of dealing with things, people, and events is rarely based solely on nonsense.

Old-fashioned library card catalog https://www.flickr.com/photos/mamsy/ [CC BY 2.0, via Wikimedia CommonsWhy not? Because the world is not an entirely unpredictable place. What happens to us, good or bad, is seldom purely random or plain crazy. Life actually does have patterns that can be real enough, although they can also be far from clear-cut and hard to see. Even so, patterns can be categorized. Not always successfully (just ask any weather forecaster), but that doesn’t mean we shouldn’t try to do so.

But this is enough about categorical thinking for now. I want to move on and write instead about what I have previously referred to as relational thinking.

Relational thinking

The National Council of Teachers of Mathematicsdefines this way of thinking as the “mindful application of place value and the properties of number, operations, and equality in solving mathematics problems.” If this confuses you as much as it does me, note this organization adds: “A student with a disposition toward relational thinking has a habit of thinking before acting.”

This seems like an uncommonly low bar. Certainly not the definition I have in mind. Nature‘s online magazine Science of Learning offers an alternative: “At the core of all human learning and performance . . . is the foundational ability to perceive patterns that thread through all of nature, including human nature.”

This isn’t quite it, either. In fact, to me this sounds more like a definition of categorical thinking. So let me give you my own take on what pairing these two words together means:

Categorical thinking assumes things exist apart from one another, and may then become connected with one another.
Relational thinking assumes instead things exist because they are connected.

If my definition sounds too mystical to you, let me offer you several examples of what I mean.

One-sided relationships

It seems likely that no relationship is solely one-sided if looked at closely enough. While granting this likelihood, there is no doubt that relationships can be so out of balance that it is not just a technicality that one side is more influential than the other. Critically, the character and perhaps the very existence of one side in such an imbalanced relationship may depend, maybe entirely, on the relationship it has with the other side.

A classic example of such a one-sided connection is the relationship between the Sun in our solar system and all the other planets (and then some) revolving around it, including Planet Earth.

Even without venturing into the exotic realm of modern cosmological theories about quantum gravity, it is obvious enough nowadays except perhaps to those who believe the Earth truly is flat that if it were not for the gravitational relationship between the planets and our Sun, the Earth would not exist at all and neither would we. Our reliance on the Sun is that one-sided and decisive. There would also be no life at all on our planet without the Sun serving as life’s ultimate source of energy, however otherworldly such a statement may sound.

Technical note: In formal network analysis, a relationship between two things (the two nodes or vertices in the relationship) is said to be dyadic (two-sided). When both are taken together, they are called a dyad. Furthermore, such two-party connections can be either undirected (more or less balanced or symmetrical from the point of view of each), or they can be directed (each party has a different take on the relationship). From this perspective, the relationship between the Earth and the Sun is a directed dyadic relationship, and it is a relationship that is decidedly one-sided.

Two-sided relationshps

It has been said that human beings have an innate sense of fairness and an ingrained willingness to do something for others when they are reasonably confident that a favor, whatever it is, will be returned, if not in kind, at least in some other way having equal value.

This judgment of our willingness to engage with others in two-sided relationships is far too cynical. Available evidence suggests instead that most of us are basically predisposed to be kind, collaborative, and helpful to others. That’s how we have evolved as a social species.

Moreover, humans as a rule are not only ready, willing, and able to forge and maintain relationships with others. We are also remarkably skilled at coming up with playful excuses to do so.

Although jogging, bicycling, and other forms of exercise, for instance, can be done easily enough as solitary tasks, people often find ways of turning even such seemingly self-centered healthy activities into broadly social occasions.

Although a more sedentary activity than a physically healthful one, this observation holds true also for online computer gaming, which is now a major leisure-time social activity for millions around the globe.

Technical note: A racket sport such as tennis is an example of an undirected dyadic relationship (accepting, of course, that only one of the players can win). Yet tennis is also a spectator sport, and as such, creates a directed dyadic relationship between sports fans and players.

Many-sided relationships

It is obvious enough that spectator sports such as tennis or baseball involve more than just simple dyadic relationships between players and spectators. The social complexity of team sports is even more apparent for sports such as soccer and football that call for the coordination of players both within and between the two opposing teams on the field.

A friend in need, 1903. Public domain, via Wikimedia Commons

Side note: There seem to be few team sports that call for more than two teams on the playing field at the same time—maybe they should be called “dyadic sports”—although a few examples do come to mind if you are willing to bend the definition of what is a sport: many kinds of card games, many types of board games, some varieties of billiards, some forms of bicycle racing, etc.

But the many-sided complexity of most human relationships isn’t just obvious while watching players interact with one another on a playing field. The general complexity of human relationships is more than apparent also among the fans watching the game being played right there before their eyes. Indeed, in the case of some sports, it could be argued that “most of the action” is actually in the bleachers, not down on field. (You may be able to tell I don’t like baseball, and I am not too fond of football, either.)

How can we tackle the complexity of human relationships?

Classic definitions of social network analysis as a way of coming to grips with the complexity of human social relationships commonly read like this one from John Scott’s highly successful book Social Network Analysis: A Handbook: “social network analysis is an orientation towards the social world that inheres in a particular set of methods. It is not a specific body of formal or substantive theory” (page 37, 2nd ed., Sage Publications, 2000).

I find such a view naive, however well-intentioned. It is quite impossible to isolate methods from theories and then claim to be doing good science. This is an observation I will explore further in the next posting in this series.

June 2, 2018

AS NOTED EARLIER THIS WEEK at SCIENCE DIALOGUES, the popular science monthly Scientific American has now published a lengthy and decidedly critical commentary on current practice in the new field of paleogenetics .

At present it looks like the hype promoting paleogenetics research far exceeds the actual performance.

But who knows what the future will bring once human geneticists realize that there are no simple ways to connect the dots between human genes and the realities of human history.